{"id":"5951953f-d4a2-4a79-81aa-161491b99a97","arxiv_id":"2501.13006","paper_version":1,"verdict":"CONDITIONAL","confidence":"LOW","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A THz integrated sensing, communications, and powering system can be jointly optimized over sensing time and power-splitting ratio, with the optimum found by divide-and-conquer search over a constrained region.","lead":"This paper optimizes the time spent sensing a receiver's beam alignment and the power split between data and energy transfer in a terahertz link, maximizing data rate or harvested energy under a constraint on the other. It is a numerical systems-level study about allocating resources in a three-way sensing, communications, and powering system for 6G.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Received power formula squares a power-based misalignment factor, invalidating reported optima.","rationale":"The reader's weakest assumption (unvalidated exponential misalignment decay) is legitimate, but the double-counting of hmis in Eq. (20) is a stronger, internal error: it contradicts the cited pointing-error model and changes the core objective functions. Even if the exponential law were replaced by a realistic control-loop model, the correct power expression must still contain hmis only once. I therefore disagree with the reader's identification of the weakest link. The central claim of a trade-off and joint optimum is not disproven by this error, since the optimization procedure would still find a maximum for a corrected model; however, the specific numerical values and design insights are unreliable until Eq. (20) is fixed and results are recomputed. The verdict CONDITIONAL remains appropriate, but the required revision should be expanded to include this modeling correction.","tokens_in":75,"tokens_out":10395,"duration_ms":111791,"concrete_test":"Re-derive Eq. (20) using the standard pointing-error model of [34]: h_p = A0 exp(-2 r^2 / w_eq^2) is a power fraction, so Pr = Pt Gbs-t Gr PL(d) habs hmis |hf|^2 ηb, with hmis as in Eq. (13). Re-run the optimization in Section III (Algorithms 1 and 2) with this corrected Pr and the Table I parameters. If the optimal (ρ0, ρ1) and E*, R* change, the reported numbers do not follow from the stated model; compare the new maxima with the claimed (0.28, 0.84) and (0.28, 0.81).","verdict_should_be":"UNCHANGED","load_bearing_attack":"Equation (20) computes received power as Pr = Pt Gbs-t Gr PL(d) habs |hmis|^2 |hf|^2 ηb, where hmis from Eq. (13) already includes the power attenuation factor S0 = erf(ε)^2 and exp(-2 lmis^2 / Rebw^2). In the cited pointing-error model [34], [35], hmis is the fraction of power collected, not a field amplitude. Squaring it doubles the exponent of the misalignment loss (to -4 lmis^2 / Rebw^2) and squares S0, which changes the sensitivity of Pr to sensing time and therefore alters the optimal (ρ0, ρ1). All subsequent derivatives (Eqs. (28)-(37)), the feasibility sets (40)-(41), and the reported maxima E* = 3.63386 W·s at (0.28, 0.84) and R* = 1519.1 bits/Hz at (0.28, 0.81) are computed from this expression. This is an internal inconsistency with the cited model, independent of the (also plausible) concern about the exponential decay law in Eq. (25).","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper considers a terahertz integrated sensing, communications and powering (THz-ISCAP) system in which a fraction ρ0 of a fixed time frame is used for sensing/beam alignment and the remaining time is used for SWIPT, with the received power split between information decoding and energy harvesting by a ratio ρ1. It models THz propagation using aperture gains, free-space/Fresnel path loss, molecular absorption, beam misalignment, Rician fading, beam collection efficiency and a nonlinear RF-to-DC conversion model. It formulates two constrained optimization problems: maximize harvested energy subject to a rate constraint and maximize rate subject to an energy constraint. Using monotonicity/unimodality arguments and divide-and-conquer/bisection algorithms, it reports numerical optima, e.g., E* = 3.63386 W·s at (ρ0*, ρ1*) = (0.28, 0.84) under R ≥ 1500 bits/Hz, and R* = 1519.1 bits/Hz at (0.28, 0.81) under E ≥ 3.5 W·s. The paper also numerically studies the effects of frequency, distance and aperture diameter.","tokens_in":19277,"tokens_out":9909,"duration_ms":98044,"significance":"The ISCAP concept is timely, and the paper brings together a broad set of THz channel effects, including near-field path loss, molecular absorption, nonlinear energy harvesting and beam misalignment, in a single resource-allocation formulation. If the modeling and optimization were correct, the paper would provide a useful starting point for sensing-assisted THz SWIPT design. However, several load-bearing modeling choices are either inconsistent with the cited channel models or are adopted without justification, and the reported numerical optima are therefore not reliable as they stand. The problems are identifiable and in principle correctable, but the central quantitative claims require substantial rework. The paper does not provide machine-checked proofs or reproducible code, and the analytic optimality claims are not currently established in a verifiable form.","major_comments":[{"comment":"In Eq. (13), hmis is taken from the pointing-error model of [34], [35], where S0 exp(-2 lmis^2 / Rebw^2) is the fraction of power collected at the receiver. Eq. (20) then multiplies by |hmis|^2, producing exp(-4 lmis^2 / Rebw^2) and S0^2. This double-counts the misalignment loss and changes the derivative with respect to ρ0, and hence the feasible sets (40)-(41) and the reported optima (E* = 3.63386 W·s at (0.28, 0.84) and R* = 1519.1 bits/Hz at (0.28, 0.81)) are all computed from an internally inconsistent received-power expression. Eq. (21) has the same problem in the reflected path. The authors should use hmis, not |hmis|^2, in (20) and (21), and then recompute all analytical and numerical results.","section":"II.A.4, Eqs. (13) and (20)"},{"comment":"In Section III.B, ρ1 is defined as the fraction of the received power used for energy harvesting. The input to the RF-to-DC converter is then ρ1Pr, so in the nonlinear model (18) the harvested DC energy should be (1 - ρ0)T fη(ρ1Pr), not (1 - ρ0)T ρ1 fη(Pr) as written in (26). The energy-constraint derivation in (46) repeats the same error by evaluating fη at the full received power and then multiplying by ρ1. Since fη is nonlinear, these expressions are not equivalent, and both the feasible region and the optimal solution change. Please correct (26) and the E ≥ Eε constraints in Section III.C.4, and recompute the affected numerical results.","section":"III.B, Eqs. (26) and (46)"},{"comment":"The exponential decay model lmis(t) = l0 exp(-αt) is introduced as a simplification without a physical or protocol-based justification; α and l0 are effectively free parameters in Table I, and no sensitivity analysis is given. The existence and value of the optimal sensing-time ratio ρ0* are direct consequences of this assumed decay law, so the main trade-off result is not robustly established. Please either justify the model by connecting it to a specific beam-alignment/control procedure or provide sensitivity results showing how ρ0* and the rate-energy frontier change over plausible ranges of α and l0.","section":"III.A, Eq. (25)"},{"comment":"The analytic derivations are not reliable in their current form. Examples include the malformed Hessian notation '∂fE^2/∂^2ρ1' in Section III.C; Eq. (36), which contains a logarithmic argument with e^{-2αρ0T} even though the expression is evaluated at ρ0 = 0; and Eq. (35), where R_ebw^2 appears in denominators that seem to belong in different factors and some terms appear to be missing factors of ln(2). Because the sign claims ∂h/∂ρ0 < 0 and h(0) > 0 are stated as 'it is found' on the basis of these garbled expressions, the claimed unimodality and the validity of the bisection/divide-and-conquer optimizers are not established. Please rewrite all partial derivatives with consistent notation and provide a step-by-step verification of the monotonicity and unimodality properties used to justify the algorithms.","section":"III.C, Eqs. (28)-(37)"},{"comment":"Algorithms 1 and 2 are under-specified. The while loops say 'while Stopping criterion not met do' without defining the stopping criterion; lines 9-13 of Algorithm 1 contain assignments such as 'p1 ← (...) = 1', which are not well-formed; and the claim that the optimal ρ1 lies on the upper or lower boundary of the feasible sets (41), (49) or (54) is not proven. Since the paper's central claim is optimality of the reported (ρ0*, ρ1*), the algorithms need to be fully specified, and their correctness and convergence need to be argued or numerically verified.","section":"III.C, Algorithms 1 and 2"}],"minor_comments":[{"comment":"Please clarify the unit convention for R: the expressions have the dimension of bits per second per Hz multiplied by seconds, so the reported unit 'bits/Hz' should either be justified or changed to 'bits'.","section":"Eqs. (22) and (27)"},{"comment":"The notation for optima is inconsistent (e.g., ρ0∗ vs. ρ0*, ρ1∗ vs. ρ1*), and some derivative expressions such as '∂fE^2/∂^2ρ1' are malformed; a consistent mathematical notation would improve readability.","section":"Throughout"},{"comment":"The captions mention 'shadow area' and specific markers (diamond, triangles, circle), but the reader must infer these from the figures; adding a legend or a more descriptive caption would make the feasible regions and the reported optima easier to verify.","section":"Figs. 5 and 6"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is readable and the ISCAP idea is relevant, but the numerical contributions currently rest on several technical errors and unverified analytical claims. In my assessment the errors are fixable, so I recommend major revision rather than rejection. In addition to the points in the report, I would ask the authors to add a comparison with simple baselines (e.g., fixed sensing time, equal power splitting, or no sensing), because the practical benefit of the claimed optimal scheduling is not quantified. The statement that THz-ISCAP has not been studied except in [23] should also be softened, since prior ISCAP work at lower frequencies is cited and the novelty is primarily the THz-specific modeling."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Read this one if you want a quick picture of where THz-ISCAP is heading; just don't trust the numbers yet.\n\nWhat's new: the combination of sensing-driven beam alignment with SWIPT time/power splitting in the THz band, and the joint optimization of the sensing time ratio and power-splitting ratio. The prior ISCAP papers don't use THz, and the THz ISAC/SWIPT papers don't do this alignment-assisted joint split. The paper is also honest about its parameters and gives a full sweep over frequency and aperture size. The frequency glitches around 184/326/381/449 GHz in Fig. 10 are a nice touch, and the literature coverage looks right.\n\nThe soft spots are real. First, the received-power model in Eq. (20) squares hmis from Eq. (13), but that hmis is already a power-collection factor (S0 = erf(ε)^2, from the cited pointing-error model [34],[35]). Squaring it doubles the misalignment exponent to -4 lmis^2/Rebw^2 and squares S0, which changes how Pr responds to sensing time and therefore changes the claimed optima. If the authors meant hmis to be an amplitude, then S0 should be erf(ε), not erf(ε)^2. Either way there is an internal inconsistency with their own cited model, and the reported E*=3.63386 W·s and R*=1519.1 bits/Hz are computed from that expression. Second, the analytic unimodality claims are asserted with derivative expressions (28)-(37) that are visibly corrupted—misplaced denominators, missing terms—and the claims that g(0)>0 and h(0)>0 'in general' are not proven. The bisection method needs a real argument that a unique root exists over the whole parameter range. Third, the exponential misalignment decay law in Eq. (25) is ad hoc, with α and l0 free parameters; the authors admit it is a simplification, but the optimal sensing time depends on it, so the design insights are conditional on that curve.\n\nWho's this for: people working on THz ISAC/SWIPT or 6G resource allocation. As a problem formulation and a parameter-sweep template, it has value. The flaws are fixable. I would not cite the numbers as they stand, but I would send it to peer review with a clear request to fix the pointing-error model, re-derive the derivatives, and either justify the alignment decay law or present the results as illustrative. If the authors do that, it could be a decent systems paper.","headline":"A useful THz-ISCAP problem formulation with a transparent parameter sweep, but the received-power model squares a power-based misalignment factor and the analytic claims are unproven, so the reported optima are not reliable.","tokens_in":19829,"tokens_out":4192,"would_cite":false,"duration_ms":41480,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"In a THz integrated sensing, communications, and powering system, jointly optimizing the sensing time ratio and the power splitting ratio maximizes achievable rate or harvested energy while meeting a constraint on the other, and numerical…","keywords":["terahertz","integrated sensing communications and powering","6G","beam misalignment","simultaneous wireless information and power transfer","rate-energy trade-off","time allocation","molecular absorption"],"falsifier":"Run a THz beam-alignment loop with the paper's parameters and record the misalignment error lmis over time; if the measured decay deviates substantially from l0 $e^{{−0.1 t}}$ (for example, it has a floor above zero or a different rate), recompute the optima and compare them with ρ0*=0.28 and E*=3.63386 w·s under the 1500 bits/Hz rate constraint.","tokens_in":18853,"feed_emoji":"📡","tokens_out":4416,"duration_ms":46836,"temperature":0.7,"pith_summary":"This paper proposes a terahertz integrated sensing, communications, and powering (THz-ISCAP) system in which sensing is used to reduce beam misalignment before simultaneous wireless information and power transfer. It tries to establish that, for a fixed time frame, there is an optimal sensing time ratio and an optimal power splitting ratio that jointly maximize the harvested energy subject to a rate requirement, or the achievable rate subject to an energy requirement. The authors derive monotonicity properties that allow efficient numerical optimization, and they report concrete optima: with a rate constraint of 1500 bits/Hz, maximum harvested energy is 3.63386 w·s at (0.28, 0.84); with an energy constraint of 3.5 w·s, maximum rate is 1519.1 bits/Hz at (0.28, 0.81). They also show that higher THz frequency and larger transmit aperture improve both energy and rate in the studied range, and that certain absorption frequencies cause dips in performance. These results suggest that sensing time and power splitting can serve as tuning knobs for balancing communication and energy delivery in future 6G THz networks.","feed_headline":"Sensing-time and power-split tuning peaks THz 6G performance","feed_subtitle":"A two-knob optimization—sensing time and power splitting—finds the best rate-energy balance for terahertz links.","key_machinery":"The central mechanism is the exponential misalignment decay model, lmis(t)=l0 $e^{{−α t}}$, which converts sensing time into improved beam alignment and therefore into received power. Combined with the power-splitting ratio ρ1, this gives harvested energy E and achievable rate R as functions of (ρ0, ρ1); the paper shows that E increases with ρ1, R decreases with ρ1, and both increase then decrease with ρ0, so that the constrained optima lie at interior points found by bisection and a divide-and-conquer search. Supporting components are the aperture-antenna gain, Fresnel-region path-loss correction, molecular absorption, beam collection efficiency, and a non-linear RF-to-DC conversion model.","core_discovery":"Within a two-phase THz frame—sensing first to reduce beam misalignment, then simultaneous wireless information and power transfer—the paper claims that a joint choice of the sensing time fraction ρ0 and the received-power splitting fraction ρ1 maximizes the system's performance. With a minimum rate of 1500 bits/Hz, the maximum harvested energy is 3.63386 w·s at (ρ0, ρ1)=(0.28, 0.84); with a minimum energy of 3.5 w·s, the maximum rate is 1519.1 bits/Hz at (0.28, 0.81). The paper also finds that higher THz frequencies and larger transmit apertures improve both energy and rate in the considered settings, and that both performance measures benefit from an interior, balanced optimum rather than an extreme allocation.","pith_inferences":["If real beam-alignment control does not follow the assumed exponential decay (e.g., it has a residual error floor or a different rate), the optimal sensing time will shift; a calibration campaign measuring lmis over time could directly refine or replace Eq. (25).","The same two-knob trade-off structure may extend to multi-user or RIS-assisted THz-ISCAP, but interference and coupled power constraints could break the simple monotonicity that the algorithms rely on.","The reported optimal ratios could serve as initialization points for adaptive, online tuning in a deployed system where channel conditions and alignment dynamics vary slowly.","The frequency-dependent absorption glitches observed near 184, 326, 381, and 449 GHz indicate that carrier selection should avoid these windows, which is a testable design guideline for THz-ISCAP hardware."],"forward_implications":["For any fixed frame time, the optimal sensing time and power splitting ratios need not be extreme; an interior balance point exists and is computable by the proposed algorithms.","The reported optimum is consistent across the two tested objectives: ρ0*=0.28 appears in both energy-maximization and rate-maximization, suggesting a relatively robust sensing-time design rule.","Higher THz frequency, despite greater path loss and molecular absorption, improves harvested energy and achievable rate when gain and beam collection efficiency are included, indicating that THz bands can be attractive for ISCAP.","Larger transmit aperture diameters increase both E and R in the studied parameter window, providing a concrete hardware-design lever.","The optimization approach reduces the two-dimensional search to a one-dimensional traversal, lowering computational complexity for practical implementation."],"supporting_citations":[{"why":"Supplies the sensing-assisted control process and the idea that misalignment error can be modeled as exponentially decreasing with sensing time.","marker":"[24]"},{"why":"Provides the aperture antenna gain definition used in Eqs. (1)–(4).","marker":"[25]"},{"why":"Gives the Fresnel-region path-loss model and the boundary distances that define the reactive and radiating near-field regions.","marker":"[27]"},{"why":"Provides the empirical correction to the Friis formula in the Fresnel region, used for γA in Eq. (8).","marker":"[30]"},{"why":"Supplies the 100–450 GHz line-of-sight channel model with molecular absorption coefficients used in Eqs. (11)–(12).","marker":"[32]"},{"why":"Gives the Gaussian beam radius formula W(d) used to compute the equivalent beam width in Eq. (24).","marker":"[38]"},{"why":"Defines the beam collection efficiency used in Eq. (17).","marker":"[40]"},{"why":"Provides the non-linear RF-to-DC conversion curve used to compute harvested DC energy in Eqs. (18)–(19).","marker":"[42]"}],"fun_headline_variants":["Joint sensing-splitting optimisation peaks THz 6G","Balanced sensing-time and power-split maxes THz 6G","Sensing and power-split balance boosts THz rate and energy","Optimal sensing power balance for THz integrated links"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that beam misalignment error shrinks exponentially with sensing time according to lmis(t)=l0 $e^{{−α t}}$ with fixed constants l0=0.8 and α=0.1; if real alignment does not follow that curve, the optimal sensing time and the whole rate-energy trade-off change.","fun_headline_variants_meta":{"raw":{"variants":["Joint sensing-splitting optimisation peaks THz 6G","Balanced sensing-time and power-split maxes THz 6G","Sensing and power-split balance boosts THz rate and energy","Optimal sensing power balance for THz integrated links"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000228,"raw_usage":{"total_tokens":1444,"prompt_tokens":886,"completion_tokens":558,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":502,"completion_tokens_details":{"reasoning_tokens":485}},"tokens_in":502,"tokens_out":558,"duration_ms":6077,"temperature":1.0,"reasoning_tokens":485,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T16:31:15.480628+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run a THz beam-alignment loop with the paper's parameters and record the misalignment error lmis over time; if the measured decay deviates substantially from l0 $e^{{−0.1 t}}$ (for example, it has a floor above zero or a different rate), recompute the optima and compare them with ρ0*=0.28 and E*=3.63386 w·s under the 1500 bits/Hz rate constraint.","supporting_citations":[{"cited_title":"Integrated Scheduling of Sensing, Communication, and Control for mmWave/THz Communications in Cellular Connected UA V Networks,","cited_arxiv_id":null,"evidence_quote":"Supplies the sensing-assisted control process and the idea that misalignment error can be modeled as exponentially decreasing with sensing time."},{"cited_title":"IEEE Standard for Definitions of Terms for Antennas,","cited_arxiv_id":null,"evidence_quote":"Provides the aperture antenna gain definition used in Eqs. (1)–(4)."},{"cited_title":"Study of the feasibility of using microwave power transfer for dynamic wireless electric vehicle charging,","cited_arxiv_id":null,"evidence_quote":"Gives the Fresnel-region path-loss model and the boundary distances that define the reactive and radiating near-field regions."},{"cited_title":"Generalised correction to the Friis formula: quick determination of the coupling in the Fresnel region,","cited_arxiv_id":null,"evidence_quote":"Provides the empirical correction to the Friis formula in the Fresnel region, used for γA in Eq. (8)."},{"cited_title":"A line-of-sight channel model for the 100–450 gigahertz frequency band,","cited_arxiv_id":null,"evidence_quote":"Supplies the 100–450 GHz line-of-sight channel model with molecular absorption coefficients used in Eqs. (11)–(12)."},{"cited_title":"Microwave and Millimeter Wave Power Beaming,","cited_arxiv_id":null,"evidence_quote":"Defines the beam collection efficiency used in Eq. (17)."},{"cited_title":"Wireless Energy Harvesting Using Signals from Multiple Fading Channels,","cited_arxiv_id":null,"evidence_quote":"Provides the non-linear RF-to-DC conversion curve used to compute harvested DC energy in Eqs. (18)–(19)."}],"review_version":1}